TY - GEN
T1 - Stability by averaging of linear discrete-time systems
AU - Jbara, Adam
AU - Katz, Rami
AU - Fridman, Emilia
N1 - Publisher Copyright:
© 2024 EUCA.
PY - 2024
Y1 - 2024
N2 - Recently, a constructive approach to averaging-based stability was proposed for linear continuous-time systems with small parameter ϵ > 0 and rapidly-varying almost periodic coefficients. The present paper extends this approach to discrete-time linear systems with rapidly-varying periodic coefficients. We consider linear systems with state delays, where results on the stability via averaging are missing. Differently from the continuous-time, our linear matrix inequalities (LMIs) are feasible for any delay (i.e. the system is exponentially stable) provided E is small enough. We introduce an efficient change of variables that leads to a perturbed averaged system, and employ Lyapunov analysis to derive LMIs for finding maximum values of the small parameter ϵ > 0 and delay that guarantee the exponential stability. Numerical example illustrates the effectiveness of the proposed approach.
AB - Recently, a constructive approach to averaging-based stability was proposed for linear continuous-time systems with small parameter ϵ > 0 and rapidly-varying almost periodic coefficients. The present paper extends this approach to discrete-time linear systems with rapidly-varying periodic coefficients. We consider linear systems with state delays, where results on the stability via averaging are missing. Differently from the continuous-time, our linear matrix inequalities (LMIs) are feasible for any delay (i.e. the system is exponentially stable) provided E is small enough. We introduce an efficient change of variables that leads to a perturbed averaged system, and employ Lyapunov analysis to derive LMIs for finding maximum values of the small parameter ϵ > 0 and delay that guarantee the exponential stability. Numerical example illustrates the effectiveness of the proposed approach.
UR - http://www.scopus.com/inward/record.url?scp=85200565891&partnerID=8YFLogxK
U2 - 10.23919/ECC64448.2024.10591101
DO - 10.23919/ECC64448.2024.10591101
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AN - SCOPUS:85200565891
T3 - 2024 European Control Conference, ECC 2024
SP - 1662
EP - 1667
BT - 2024 European Control Conference, ECC 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 European Control Conference, ECC 2024
Y2 - 25 June 2024 through 28 June 2024
ER -